Dynamically tunable hydrodynamic transport in boron nitride-encapsulated graphene

TL;DR

This work demonstrates a reversible, UV-assisted method to dynamically tune disorder in hBN-encapsulated graphene, enabling continuous control over the balance between momentum-conserving electron-electron interactions and momentum-relaxing scattering at room temperature. Using Johnson-noise thermometry and transport measurements, the authors show a tunable transition between viscous (hydrodynamic) and diffusive regimes, evidenced by a pronounced departure from and subsequent restoration of the Wiedemann–Franz law as disorder is varied. The study quantifies how disorder modifies the Lorentz number, extracts impurity-scattering parameters, and reveals distinct thermal and Fermi-liquid behaviors of shear viscosity, highlighting a practical platform for testing relativistic hydrodynamics in Dirac materials. The ability to reversibly modulate disorder in a single device offers a powerful avenue to explore disorder-enabled hydrodynamics and the fundamental interplay of momentum-conserving and momentum-relaxing processes in graphene.

Abstract

Over the past decade, graphene has emerged as a promising candidate for exploring the viscous nature of electronic flow facilitated by the availability of extremely high-quality devices employing a graphene channel encapsulated within dielectric layers of hexagonal boron nitride (hBN). However, the level of disorder in such systems is mainly determined by the device fabrication protocols, making it impossible to obtain a tunability between the impurity-dominated and the viscous transport within the same device. In this work, using a combination of ultraviolet (UV) radiation and gate electric field, we have demonstrated a dynamic modulation of charge hydrodynamics, quantified in the thermal and electrical transport by the extent of departure from the Wiedemann-Franz (WF) Law in monolayer graphene devices at room temperature. We achieved this by tuning the disorder level continuously and reversibly using UV light to create transient trap states in the encapsulating hBN dielectric. With progressive UV radiation, we observed a dramatic increase in the momentum-relaxing scattering relative to that between the electrons and also the Lorentz number, by nearly a factor of ten, with increasing disorder, thereby approaching the restoration of the WF law in highly disordered graphene. Our experiments outline a potent strategy to tune the fundamental mechanism of charge flow in state-of-the-art graphene devices.

Figures (4)

• Figure 1: Tuning electronic disorder using UV radiation: (a). Top-left corner shows the optical micrograph of one of the measured devices (D3). The cross-sectional view of the heterostructure is shown to its right. [Below] Schematic of the experimental setup used for performing UV radiation-based tuning of disorder. (b) Different mechanisms responsible for charge redistribution upon UV illumination (indicated using thick white arrows with black border). Process 1 refers to UV-induced photogating, which results in the transfer of charges from hBN to graphene or vice versa. Process 2 indicates the formation of charge puddles in the mid-gap states of hBN as a result of UV excitation. Process 3 marks the onset of UV-induced activation of trap states at the hBN-SiO$_2$ interface and subsequent random trapping of charges at those sites. The blue-coloured charges are intrinsic charges residing in the different layers, while the yellow-coloured ones are the UV radiation-induced charges which have been redistributed across the heterostructure. (c) Variation of four-terminal resistance $R_\mathrm{4p}$ as a function of gate voltage $V_\mathrm{G}$ for both forward and backward $V_\mathrm{G}$ sweeps at four different values of $V_\mathrm{PD}$. The panel at the bottom shows the characteristics obtained by resetting the device to pristine condition (indicated by a vertical dotted line) by shining UV radiation at $V_\mathrm{PD} = 0$ V. (d) Variation of electrical conductivity ($\sigma$) with $n$ in device D3 for different values of $V_\mathrm{PD}$. The resulting $n_\mathrm{min}$ for each of these traces has been obtained by noting the intersection between the lines $\sigma = \sigma_\mathrm{min}$ (dotted line) and $\sigma \propto n^{0.75}$ (dashed line), where $\sigma_\mathrm{min}$ is the electrical conductivity at the Dirac point. (e) Variation of the total scattering rate $\tau^{-1}$ as a function of $n$ for different values of $V_\mathrm{PD}$. The dashed line shows the variation of electron-electron relaxation scattering rate $\tau_\mathrm{ee}^{-1}$ with $n$. The $n<n_\mathrm{min}(0)$ region is colored with light red, whereas $n_\mathrm{min} (0) \le n \le n_\mathrm{min}$ region is colored with light blue. (f) Variation of the momentum relaxation scattering rate $\tau_\mathrm{mr}^{-1}$ as a function of $n$ for the same values of $V_\mathrm{PD}$, as those depicted in panel (e). The solid line indicates a $\sqrt{n}$ dependence. (g) Ratio of momentum relaxation scattering rate ($\tau_\mathrm{mr}^{-1}$) to the electron-electron scattering rate ($\tau_\mathrm{ee}^{-1}$) as a function of $n_\mathrm{min}$ for two different carrier densities. The solid lines vary as $n_\mathrm{min}$ and serve as a guide to the eye. The colored region corresponding to $\tau_\mathrm{mr}^{-1}/\tau_\mathrm{ee}^{-1} < 1$ indicates the viscous limit, while the region with $\tau_\mathrm{mr}^{-1}/\tau_\mathrm{ee}^{-1} > 1$ indicates the diffusive limit.
• Figure 2: WF law violation as a signature of electron hydrodynamics: (a) Variation of $\sigma$ as a function of $n$ for three different devices D1, D2 and D3. The solid line (colored in black) indicates a $\sqrt{n}$ dependence and serves as a guide to the eye. $n_\mathrm{min}$ and $n_\mathrm{min}(0)$ have been indicated using vertical solid lines. The area shaded in light pink indicates $n < n_\mathrm{min}(0)$. (b) Variation of $\sigma - \sigma_\mathrm{min}$ as a function of $n$ for three traces shown in (a). The solid line (colored in black) indicates a $n^2$ dependence and serves as a guide to the eye. The area shaded in light pink indicates $n < n_\mathrm{min}(0)$. (c) Schematic of the electrical circuit used for Johnson noise thermometry measurements. (d) Variation of $T_\mathrm{e}$ as a function of $E$ for D2, at three different carrier concentrations given by $n (10^{12}$ cm$^{-2}) = 0.2, 0.4, 0.6$. (e) Variation of $\mathcal{L}/\mathcal{L}_\mathrm{WF}$ as a function of $n$ for three devices, D1, D2 and D3, all in pristine condition. The solid curves refer to the Lorentzian fit of the data, as per Eqn. \ref{['L']}. The error bars associated with the data points represent the standard deviation of results obtained from the experiment.
• Figure 3: Signature of dynamically-tunable electron hydrodynamics in thermal transport: (a) Variation of $\mathcal{L}/\mathcal{L}_\mathrm{WF}$ as a function of n for device D3 at different values of $V_\mathrm{PD}$. The solid curves refer to the Lorentzian fits of the data, as per Eqn. \ref{['L']}. The error bars associated with the data points represent the standard deviation of results obtained from the experiment. (b) $\mathcal{L}/\mathcal{L} (n=0)$, where $\mathcal{L}(n=0)$ refers to the value of $\mathcal{L}$ at the CNP, as a function of $n$ for three different scenarios: (Left) Pristine graphene, (Center) After the pristine graphene has been UV-irradiated with $V_\mathrm{PD} = -40$ V, (Right) After the UV-irradiated graphene is again subjected to UV radiation with $V_\mathrm{PD} = 0$ V, thereby restoring the pristine conditions. The FWHMs ($n_0, n_0^*, n_0^{**}$) of the Lorentzian fits and the comparison of their magnitudes are mentioned near the bottom of each panel. The error bars presented here indicate the standard deviation of the experimental data points. (c) Variation of $n_0$ as a function of $n_\mathrm{min}$ for device D3. (d) Variation of $\mathcal{L}/\mathcal{L}_\mathrm{WF}$ as a function of $n_\mathrm{min}$ for device D3, part of which has been shown in (a). The three panels refer to three distinct carrier density regimes: hole-doped (Left), CNP (Center) and electron-doped (Right). The dashed line refers to $\mathcal{L}/\mathcal{L}_\mathrm{WF} = 1$. The error bars presented reflect the standard deviation of the experimental data points.
• Figure 4: Effect of disorder on shear viscosity in the Fermi liquid and thermal regimes: (a) $\eta_\mathrm{FL}/n$ as a function of $\tau_\mathrm{mr}^{-1}/\tau_\mathrm{ee}^{-1}$ for different carrier densities, indicated using symbols of different color. The horizontal dashed line points towards the asymptotic tendency of $\eta_\mathrm{FL}/n$. In the diffusive limit, the solid line indicates $\eta_\mathrm{FL}/n \propto \tau_\mathrm{mr}^{-1}/\tau_\mathrm{ee}^{-1}$ and serves as a guide to the eye. [Inset] $\eta_\mathrm{FL}$ as a function of $\tau_\mathrm{mr}^{-1}/\tau_\mathrm{ee}^{-1}$ for different carrier densities. The vertical dotted line indicated by $\tau_\mathrm{mr}^{-1}/\tau_\mathrm{ee}^{-1} = 1$ highlights the hydrodynamic-to-diffusive crossover. (b) The plot of $\sigma - \sigma_\mathrm{min}$ as a function of $n$ for three different values of $V_\mathrm{PD}$ in device D3. The solid lines scale as $n^2$ and serve as guides to the eye. The two dashed lines denote $n_\mathrm{min}$ and $n_\mathrm{min}(0)$, with the enclosed region indicating the thermal regime being colored in blue. (c) Shear viscosity in the thermal regime ($\eta_\mathrm{th}$) as a function of $n_\mathrm{min}$ in device D3. The colored region highlights the range of variation of $\eta_\mathrm{th}$. The error bars presented here indicate the standard deviation of the variable. (d) $\sigma_\mathrm{Q}$ as a function of $T_\mathrm{F}/T$ for device D3 at different values of $V_\mathrm{PD}$. (Inset) $\sigma_\mathrm{Q}$ for $T_\mathrm{F}/T \rightarrow 0$ as a function of $n_\mathrm{min}$, with a colored region indicating the range of variation of the data points. The unit along y-axis is $e^2/h$. The dashed horizontal line corresponds to $4e^2/h$.